[EM] A much simpler proportional Condocet Method - BTR-STV

[Antonio Oneala]

Abd ul-Rahman Lomax <abd at lomaxdesign.com> wrote: At 07:12 PM 5/21/2006, Antonio Oneala wrote:
>Let me be more specific.  A proportional Condorcet winner is the 
>winner of one of the segments of the populace that is represented by 
>a proportional method.  A 4 seat election represents 4 sets of 25% 
>of the populace.  There is a proportional Condorcet winner for each 25%.

I find this far less than clear. What does it mean that a segment is 
represented by a proportional method? A method doesn't represent anything....

Yes, each of four seats would, ideally, represent 25% of the 
population, if the assembly is to be a peer assembly, with each 
member equitably having the same voting power. However, this is the 
very problem we are trying to solve. If might seem that if could 
divide the electorate into N factions such that each faction had a 
Condorcet winner, then we could create a perfect proportional 
assembly with N members. However, never forget that when an election 
method has winners, it has losers. If the factions were, for example, 
randomly chosen, minorities might end up completely unrepresented.

So how would you define the factions? Mr. Oneala says, "each 25%," 
but what we have is a collection of voters, all equal to each other. 
How does one define which voter is in which faction?

Anyway, Mr. Oneala did propose a method, in the first post. I'm not 
at all sure that it produces a fair proportional result. I'll come 
back to that.

>Also, I was wrong in saying that the majority Condorcet winner will 
>always be one fo them.  Condorcet gravitates to the center point of 
>a group.  Eeach 25% may have a different center of opinion than all 
>of them coming together, since they all effect each other once they 
>come together.

Undefined is what is meant by "each" 25%. "Each" connotes something 
specific. It could simply be the first 25% to cast their votes. Or 
the votes cast in 25% of the precincts. It could be 25% chosen at 
random. Or it could be defined by some characteristic of the votes themselves.

"Center point of a group" is again, an undefined concept. There is, I 
think, a language problem here, Mr. Oneala does not seem to have 
great facility in English. I'm quite sure he is doing much better in 
English than I would do in his language, to be sure, but I think we 
need to realize that the words he is using may carry different 
meanings for him than they do for other accustomed to thinking in 
English. He may think he has explained something clearly, when it is 
far from clear to many of us.

Or the lack of clarity is in his thinking itself. And there is a 
third possibility, of course: that I am too muddled to understand...

But if I do understand what is being said, what I understand is that 
Mr. Oneala has some ideas that he has not thought through to their 
foundations, such that he can express them with precision. Perhaps 
when I examine his method and his examples, I can better understand.

 From the previous post, the method:

>Now, the mehtod I'm about to propose is a variation of 
>BTR-IRV.  BTR-IRV is a Condorcet majoritarian method.  What it is is 
>just like normal IRV, but instead of eliminating the person with the 
>least votes, you make an imaginary election between the two least 
>vote getters and use the rank ballots to eliminate the one who the 
>least people liked less than the other.

The double negation thoroughly confuses me.

However, I think this method goes like this: looking at the first 
place votes, one compares the two candidates with the least votes. 
The full ballot is examined, with all other candidates eliminated. 
The loser of this election is eliminated, then the process is applied 
recursively until all candidates have been eliminated but one. A 
Condorcet winner will win every pairwise election, so if there is a 
Condorcet winner, this method will find it.

However, if there is a cycle, i.e., there is no Condorcet winner, it 
seems to me that the method will choose a member of the Smith set. 
Which one depends on the distribution of votes on the ballots; the 
method could be quirky in that respect, because it determines which 
pair of ballots to compare by considering only first-place votes in 
the first round (or the first position votes in subsequent rounds).

>   The Condorcet winner will always win this election, and so 
> therefore will always rise to the top and be elected in the end.

The use of the definite article "the" implies that there is only one, 
that is, that there is no cycle. In any case, we are using this 
method for proportional representation and it could be possible that 
the set of voters in a "segment" is going to be chosen in such a way 
as to practically guarantee that there is a Condorcet winner. So, 
tentatively, we can assume this.

>Now, this method that I'm proposing differs slightly.  It uses a 
>normal STV method for transferring the surplus votes.  Then in the 
>elimination of undervotes round, instead of eliminating the one with 
>the least votes and then transferring their votes, you take a set of 
>the least-vote getters equivalent to the amount of seats in the 
>election, plus 1, and eliminate the one who is the least preferred 
>on the ranked ballots by the the electorate, then transfer that 
>person votes.  Therefore, a proportional Condorcet winner will never 
>be eliminated, and they will always rise to the top.

"proportional Condorcet winner" was defined as the Condorcet winner 
of a "proportional segment" of the voters. The question of how this 
segment is defined has not been addressed, at all. And, while I could 
speculate further about what he means, the connection between my 
speculations and what he actually wrote is becoming increasing tenuous.

In other words, this does not make sense to me. But perhaps when we 
look at actual vote counts, it will become clearer.


>Let's take this election as an example:
>
>Election for 2 seats, 3 candidates
>
>100: A > B > C
>10: B> C > A
>105:  C > B > A
>
>The transfer of surplus votes isn't going to change the winner, so 
>let's just ignore that part.
>
>Now, to find which person in this election we are going to eliminate 
>we take the bottom three with the least votes and compare them 
>against each other.  This is all of them in this election.  Why the 
>bottom three?  In BTR-IRV, you compare the bottom two people with 
>the least votes because it is an election for a single winner.  The 
>Condorcet winner will always win in this head to head matchup, so we 
>know he will never be eliminated.  In a multi-winner election, 
>however, this would make little sense because the majorities choice 
>would rise to the top.  No, we take an amount of candidates 
>equivalent to the amount of seats we are electing, and 1 more.
>
>To compare the candidates, in this imaginary round we simply have 
>each person "vote" for the candidate among that amount that they 
>prefer the most.
>
>That's
>
>100 for A
>10 for B
>105 for C
>
>A and C won.
>
>No additional rounds are needed, although you probably would need 
>more in a real election with a realistic amount of 
>candidates.  Note, however, that B was the majority Condorcet winner 
>here.  A and C, however, each had a majority in the set of the 
>populace that was reprented by a 2 seat election.  The amount of 
>people represented can be determined by the number of seats + 1.  It 
>would therefore be irrational to elect B, but methods like Single 
>Transferrable Vote by Condorcet loser elimination would elect B.

There was nothing in this about "segments," specifically. But we can 
imagine dividing the votes into two segments, defined by the first 
place votes, with segments being assigned, perhaps in sequence from 
the topmost vote-getter down, until the number of candidates to be 
elected has a segment. Yes, this is a division of the voters that 
elects those top two first-place vote-getters, as representatives of 
those segments, within which they are "Condorcet winners."

And in this example, if there are two to be elected, it is clear that 
these would be the best two of the three. But if there is one to be 
elected, B would be the best choice; as noted, B is the overall 
Condorcet winner.

I'm stopping here. The next example given is indeed more realistic, 
but I simply don't have time to follow it right now. If it is 
important that a method be easily explainable to the electorate -- 
and I would agree that this is quite important -- it has not been 
done here. I'd rather address the fundamental problem, which I 
imagine I can do with what brain function remains at the moment....

And I'll do that in a separate post: The use of ranked ballots for 
proportional representation.

----
election-methods mailing list - see http://electorama.com/em for list info

    You must understand, however.  I write these posts in a rather stream of thought fashion, and I actually ammended my method while I was writing though the second one.  I'm sorry if I'm being confusing, but my math is bad and election methods aren't the most clear-cut, understandable topics.  I'm a rather good writer whenever I'm writing something that makes a lot of sense to me.  

My real name is "Anthony O'Neal".  I am not Spanish.  I explained this in a previous post that you probably didn't read.  I have a feeling that you exagerrated most of my grammatical errors in the previous post based on this notion.

  The definition of the 'proportional Condorcet winner' is something that is really completely irrelevant.  The point is that this method, if I am thinking clearly, will produce Condorcet type winners in a proportional way.  If it does, in fact, work as I have said, it is an interesting alternative to CPO-STV simply because it is not as complicated. 

I read about BTR-IRV on Rangevoting.org, and I've failed to see any other mention of it anywhere.  I'm not sure where the author of the website got the idea, but it does seem important enough to him for him to bash it thouroughly, and say that Range voting is the only election method that will every plausibly work.  The only thing he did was state all of the reasons that he hated Condorcet methods and then paste them into the BTR-IRV page, so I guess this isn't very important.

So here, I will present a definition of BTR-IRV and BTR-STV here, in a way that I hope will create as little confusion as possible:

 Each "vote" is a rank-ordering of all the N candidates, for example "Nader>Gore>Bush>Buchanan" would be a possible vote (with N=4). After collecting the votes, the N-candidate election proceeds in a sequence of N-1 "rounds." In each round one candidate is eliminated and he is erased from all votes.  For example, if "Bush" were eliminated, then the above vote would become "Nader>Gore>Buchanan." 
   The one to eliminate is found as follows. Find the two candidates A and B whom the fewest voters top-rank. Now, ignoring all candidates except A and B in all the votes, i.e. based solely on the A>B and B>A relations in those votes, perform a 2-candidate majority election among A and B only. The loser of that "election" is the one we eliminate.

I propose extending this to multi-candidate elections by using this kind of elimination process instead of the straight IRV process that is currently used.  However, in the multi-winner version you cannot simply take the two candidates A and B whom the fewest voters top-rank, ignore all candidates except A and B, and then perform a 2-candidate comparison between A and B, handing the election to the candidate that most voters ranked highest.  This is a majoritarian process, and is an uncomfortable marriage between majoritarian and proportional methods.  

The amount of candidates you put into the elimination round(s)  must be based on how many people you are planning to elect.  You must put an amount of people into that round equivalent to the amount of people you are planning to elect, and 1 more.  I believe that this will ensure that the candidates the people prefer most, that is, the Condorcet winners if they exist, won't be eliminated, and if they are never eliminated...

			
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